We are given the right triangle XYZ. We know that both legs of △ XYZ measures 5 and YW is an altitude of this triangle.
Let's recall that an altitude is always perpendicular to the base of a polygon. Let's take a look at the diagram.
We can see that △ XYZ and △ YWZ have one common angle, ∠ Z. Moreover, both triangles have a right angle. Therefore, the triangles have two congruent corresponding angles. This means that △ XYZ and △ YWZ are similar by the Angle-Angle Similarity Theorem.
△ XYZ ~ △ YWZ
Recall that in the similar triangles corresponding sides are proportional.
YW/XY=YZ/XZ
To find the length of YW, we will first find the length of XZ. To do so, we will use the fact that △ XYZ is a right triangle and apply the Pythagorean Theorem.
